By: Mordechai Rubin
What Is Gematria?
Gematria (from the Greek word geometria) refers to a process by which numerical values are ascribed to the letters of the Hebrew alphabet.
As seen in the chart below, each letter, from aleph to tav, has a specific numerical value.
As a simple example, the Hebrew word אב (father) would have a numerical value of three (1+2=3). When two words or phrases have the same numerical value, this may indicate a connection. See below for the exact parameters of how this method may be applied.
Additionally, Hebrew does not make use of Arabic numerals. Therefore, numbers too are written using the Gematria system. For example, if one wanted to write the number 150, one would write ק”נ.1
Different Methods for Calculating Gematria
There are various systems for generating the numerical value of each letter (aside from the straightforward method described above). We will list some more well-known ones:
Milui — A system where each letter is spelled out. Instead of aleph being one, it is spelled out in Hebrew as אלף, resulting in a total of 111.2
Mispar Katan —Here the zeroes are removed: yud is 1, kaf is 2, kuf is 1, etc.
Atbash —Not exclusive to gematria, but used there too, Atbash is a system in which the first letter of the alef-bet (aleph) is replaced by the last letter (tav), the second letter (bet) by the second-to-last letter (shin), and so on. (The first two pairs of substitutions form the word “at-bash.”) Thus aleph would be switched with tav, and have a value of 400.3
The Orchard of Torah
Biblical interpretation falls into four general categories: peshat (the plain meaning of the text), remez (ideas hinted at by the text), derush (midrashic exposition) and sod (the mystical or esoteric teachings). Gematria would generally be included in the second of the four categories—remez. The acronym of these four elements forms the Hebrew word PaRDeS, which translates as ‘orchard’.4
Source of Gematria
The earliest source for gematria is the “Baraita of the Thirty-two Rules,” written by Rabbi Eliezer ben Rabbi Yosei HaGelili, which lists gematria as rule 28 of its 32 rules for interpreting the Bible.
There is some discussion regarding the wording of this Baraita. Some have it as ‘32 rules for interpreting the Torah,’ which would imply that these methods may be applied to derive actual laws. Others have the text ‘32 rules for interpreting Aggadah (non-legalistic elements of Torah).’
A second Mishanic source may confirm the second reading above. In chapter 3 of Pirkei Avot5 (Ethics of the Fathers) we find a reference to gematria: ‘The calculations of solar seasons and gematria are condiments of wisdom.’ Some explain this as a reference not to gematria as we understand it, but rather to general mathematics or trigonometry.6
However, Rabbi Ovadiah of Bertinoro understands this to refer to classical gematria. According to this approach, this Mishnah implies that these ideas are an addition to wisdom, not actual law itself. This is in line with the version of the Baraita above which references 32 rules for interpreting specifically the Aggadic aspects of Torah, but not the legal elements.
Can Halachah Be Derived from Gematria?
We find several instances where it seems that halachah is derived from a gematria.
For example, when an individual makes a vow to become a nazir, without specifying the length of the nezirut, the Mishnah states that the default duration is 30 days. The Talmud cites the verse “He [the nazir] shall be (יהיה) holy” as the source of this law. The Hebrew word יהיה has the gematria of 30 (yud (10) + hei (5) + yud (10) + hei (5) = 30), indicating that the default nazir period is 30 days.7
However, most commentators explain that gematria is not what informs us of the halachah in these instances. Instead, the law was already known as halachah lemoshe misinai (law given to Moshe on Mount Sinai and subsequently handed down orally). Gematria is used merely as a signal that this is indeed the law.8
General Use
Gematria is more widely used in non-legalistic (aggadic) contexts, to reveal a deeper meaning to the text. A famous example of this is the verse in Parshat Vayishlach: ‘Thus said your servant Jacob, “I have sojourned with Laban, and I have tarried until now.”9 The Hebrew word for sojourned (גרתי) has a numerical value of 613.10 Rashi11 sees this as an indication that even while living with Laban, Jacob was able to stay committed to the 613 mitzvot.12
Gematria in Kabbalistic and Chassidic texts
Gematria is an integral element of sod, the concealed aspects of the Torah. Kabbalah makes frequent use of gematria as a way of crystallizing a teaching.
As an example, in chassidic thought, the nation of Amalek—who waylaid the Jewish nation en route to Mount Sinai— symbolizes doubt without a rational explanation. Even though the entire nation had witnessed G‑d’s miraculous salvation at the splitting of the Red Sea, some still doubted. They questioned G‑d by complaining about the lack of water. This doubt created an opening for Amalek’s attack.13 The chassidic masters point out that the numerical value of Amalek (עמלק) and the Hebrew word for doubt, safek (ספק), both equal 240.14
Creation Through Gematria
According to Kabbalah, the world was created and is continuously sustained by the Ten Divine Utterances emanating from G‑d. These are the phrases G‑d used to create the world, as described in Bereshit.15 In the second volume of Tanya, Shaar HaYichud VehaEmunah, Rabbi Schneur Zalman of Liadi describes how this works:
Although the name evven (stone) is not mentioned in the Ten Utterances recorded in the Torah, nevertheless. . . the Ten Utterances descend and are progressively diminished, degree by degree, by means of substitutions and transpositions of the letters and by gematriot, which are their numerical values.16
We see that gematria plays an integral role in the creation process. Gematria is not merely a minor aspect of Torah exegesis; it has a cosmic role to play.
That said, Rabbi Schneur Zalman does point out that of the three paths of descent that the Ten Utterances undergo in the creation process (substitutions, transpositions and gematriot), gematria is the furthest removed from the original Ten Utterances.17 The other two methods are still using actual letters of the aleph-bet, whereas gematria is merely the numerical value of the letters.18
Is Every Gematria Significant?
Gematria is simple arithmetic, and anyone with a calculator can come up with some creative gematrias. Does that mean that the two words or phrases are connected? The Rebbe writes that every gematria must be sourced to be significant. If a link exists, as recognized by an appropriate authority, the numerical value can add to this association. But the gematria alone does not create a connection.19
In short, gematria is a legitimate way to interpret Torah, but only when utilized correctly.
